A319073 - OEIS

%I #29 Jan 08 2019 08:38:45

%S 1,3,2,4,6,3,7,8,9,4,6,14,12,12,5,12,12,21,16,15,6,8,24,18,28,20,18,7,

%T 15,16,36,24,35,24,21,8,13,30,24,48,30,42,28,24,9,18,26,45,32,60,36,

%U 49,32,27,10,12,36,39,60,40,72,42,56,36,30,11,28,24,54,52,75,48,84,48,63,40,33,12

%N Square array read by antidiagonals upwards: T(n,k) = k*sigma(n), n >= 1, k >= 1.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%e The corner of the square array begins:

%e          A000203 A074400 A272027 A239050 A274535 A274536 A319527 A319528

%e A000027:       1,      2,      3,      4,      5,      6,      7,      8, ...

%e A008585:       3,      6,      9,     12,     15,     18,     21,     24, ...

%e A008586:       4,      8,     12,     16,     20,     24,     28,     32, ...

%e A008589:       7,     14,     21,     28,     35,     42,     49,     56, ...

%e A008588:       6,     12,     18,     24,     30,     36,     42,     48, ...

%e A008594:      12,     24,     36,     48,     60,     72,     84,     96, ...

%e A008590:       8,     16,     24,     32,     40,     48,     56,     64, ...

%e A008597:      15,     30,     45,     60,     75,     90,    105,    120, ...

%e A008595:      13,     26,     39,     52,     65,     78,     91,    104, ...

%e A008600:      18,     36,     54,     72,     90,    108,    126,    144, ...

%e ...

%p with(numtheory): T:=(n,k)->k*sigma(n-k+1): seq(seq(T(n,k),k=1..n),n=1..12); # _Muniru A Asiru_, Jan 01 2019

%t Table[k DivisorSigma[1, #] &[m - k + 1], {m, 12}, {k, m}] // Flatten (* _Michael De Vlieger_, Dec 31 2018 *)

%o (GAP) T:=Flat(List([1..12],n->List([1..n],k->k*Sigma(n-k+1))));; Print(T); # _Muniru A Asiru_, Jan 01 2019

%Y Another version of A274824.

%Y Antidiagonal sums give A175254.

%Y Main diagonal gives A064987.

%Y Row n lists the multiples of A000203(n).

%Y Row 1 is A000027.

%Y Initial zeros should be omitted in the following sequences related to the rows of the array:

%Y Row 2-5: A008585, A008586, A008589, A008588.

%Y Rows 6 and 11: A008594.

%Y Rows 7-9: A008590, A008597, A008595.

%Y Rows 10 and 17: A008600.

%Y Rows 12-13: A135628, A008596.

%Y Rows 14, 15 and 23: A008606.

%Y Rows 16 and 25: A135631.

%Y (Note that in the OEIS there are many other sequences that are also rows of this square array.)

%Y Cf. A000203, A237593, A319526.

%K nonn,tabl,easy

%O 1,2

%A _Omar E. Pol_, Sep 22 2018